Details

analyze823.0ms (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample83.0ms (1.3%)

Algorithm

1×

intervals

Results

38.0ms	90×	body	2560	valid
27.0ms	96×	body	1280	valid
6.0ms	27×	body	640	valid
3.0ms	19×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	9×	body	80	valid

Compiler

Compiled 29 to 22 computations (24.1% saved)

simplify100.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5046	21

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 1

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
0.2b	(.f64 5 (.f64 v v))
0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `difference-of-squares_binary64`
6×	`associate-/r*_binary64`
4×	`difference-of-sqr-1_binary64`
3×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `associate-/l*_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`acos-asin_binary64` `associate-r_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

3 → 71

Calls

3 calls:

9.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
9.0ms	(.f64 5 (.f64 v v))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series13.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

6.0ms	(/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))
4.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
3.0ms	(.f64 5 (.f64 v v))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4934	1788
1	4934	1788

prune66.0ms (1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	3	81

Merged error: 0.5b

Counts

81 → 3

Compiler

Compiled 1783 to 1145 computations (35.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
8×	`swap-sqr_binary64`
6×	`associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64`
1×	`cbrt-unprod_binary64` `acos-asin_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

7.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series27.0ms (0.4%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
10.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
4.0ms	(.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))) (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))))
3.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4888	2262
1	4888	2262

prune98.0ms (1.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	93	5	98

Merged error: 0.5b

Counts

98 → 5

Compiler

Compiled 3009 to 1913 computations (36.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3) (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`sqrt-prod_binary64`
63×	`add-sqr-sqrt_binary64`
24×	`associate-l_binary64` `unswap-sqr_binary64`
18×	`unpow-prod-down_binary64` `cube-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-r_binary64` `add-exp-log_binary64`
7×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`prod-exp_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `acos-asin_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `pow-exp_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 105

Calls

4 calls:

13.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3) (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

series31.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
10.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
5.0ms	(.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3) (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))))
3.0ms	(acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1)))

simplify141.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4907	3695
1	4907	3695

prune154.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	1	2
Picked	1	0	1
Done	1	1	2
Total	117	5	122

Merged error: 0.5b

Counts

122 → 5

Compiler

Compiled 4523 to 2991 computations (33.9% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.9b	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
1.0b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
1.0b	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
1.0b	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))))

rewrite81.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

343×	`sqrt-prod_binary64`
166×	`add-sqr-sqrt_binary64`
72×	`unswap-sqr_binary64`
58×	`pow1_binary64`
55×	`associate-r_binary64`
42×	`unpow-prod-down_binary64` `cube-prod_binary64`
31×	`sqrt-pow1_binary64`
30×	`pow-prod-down_binary64`
29×	`*-un-lft-identity_binary64` `pow-prod-up_binary64` `add-cube-cbrt_binary64`
27×	`pow1/2_binary64`
25×	`associate-l_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-unprod_binary64` `sqr-pow_binary64` `prod-exp_binary64`
7×	`sqrt-unprod_binary64` `pow-sqr_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
2×	`pow-plus_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`swap-sqr_binary64` `rem-square-sqrt_binary64` `rem-sqrt-square_binary64` `pow2_binary64`

Counts

4 → 240

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))))
22.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
2.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))

series38.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
11.0ms	(.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3)))
10.0ms	(sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))
6.0ms	(.f64 (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1))))) 3))) (.f64 (sqrt.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (.f64 v v) 1)))))) (sqrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (acos.f64 (/.f64 (-.f64 1 (.f64 5 (.f64 v v))) (-.f64 (*.f64 v v) 1))))) 3))))

simplify238.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4890	15672
1	4890	15672

prune1.3s (20.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	250	2	252
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	252	5	257

Merged error: 0.5b

Counts

257 → 5

Compiler

Compiled 20849 to 14317 computations (31.3% saved)

regimes92.0ms (1.4%)

Compiler: Compiled 1010 to 720 computations (28.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	68	21
1	68	21

end0.0ms (0%)

sample2.9s (44.5%)

Algorithm

1×

intervals

Results

1.3s	3038×	body	2560	valid
693.0ms	2464×	body	1280	valid
260.0ms	1279×	body	640	valid
97.0ms	652×	body	320	valid
38.0ms	375×	body	160	valid
11.0ms	192×	body	80	valid
1.0ms	14×	body	80	nan

Compiler

Compiled 266 to 191 computations (28.2% saved)

Details

analyze823.0ms (12.8%)

sample83.0ms (1.3%)

simplify100.0ms (1.6%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite21.0ms (0.3%)

series13.0ms (0.2%)

simplify70.0ms (1.1%)

prune66.0ms (1%)

localize10.0ms (0.2%)

rewrite13.0ms (0.2%)

series27.0ms (0.4%)

simplify63.0ms (1%)

prune98.0ms (1.5%)

localize14.0ms (0.2%)

rewrite22.0ms (0.3%)

series31.0ms (0.5%)

simplify141.0ms (2.2%)

prune154.0ms (2.4%)

localize24.0ms (0.4%)

rewrite81.0ms (1.3%)

series38.0ms (0.6%)

simplify238.0ms (3.7%)

prune1.3s (20.8%)

regimes92.0ms (1.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.9s (44.5%)

Profiling